Solution: The angle between the diagonal of a square and its side is $45^\circ$, but here the angle is $150^\circ$, which lies in the second quadrant. Using the reference angle $30^\circ$, $\cos 150^\circ = -\cos 30^\circ = -\frac{\sqrt3}2$. $\boxed{-\dfrac{\sqrt3}2}$ - IX Labs